5(x-1)(x-1)=-35

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Solution for 5(x-1)(x-1)=-35 equation: 


Simplifying
5(x + -1)(x + -1) = -35

Reorder the terms:
5(-1 + x)(x + -1) = -35

Reorder the terms:
5(-1 + x)(-1 + x) = -35

Multiply (-1 + x) * (-1 + x)
5(-1(-1 + x) + x(-1 + x)) = -35
5((-1 * -1 + x * -1) + x(-1 + x)) = -35
5((1 + -1x) + x(-1 + x)) = -35
5(1 + -1x + (-1 * x + x * x)) = -35
5(1 + -1x + (-1x + x2)) = -35

Combine like terms: -1x + -1x = -2x
5(1 + -2x + x2) = -35
(1 * 5 + -2x * 5 + x2 * 5) = -35
(5 + -10x + 5x2) = -35

Solving
5 + -10x + 5x2 = -35

Solving for variable 'x'.

Reorder the terms:
5 + 35 + -10x + 5x2 = -35 + 35

Combine like terms: 5 + 35 = 40
40 + -10x + 5x2 = -35 + 35

Combine like terms: -35 + 35 = 0
40 + -10x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(8 + -2x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(8 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -2x + x2 = 0

Solving
8 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -2x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -2x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -2x + x2 = 0 + -8
-2x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-2x + x2 = -8

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -8 + 1

Reorder the terms:
1 + -2x + x2 = -8 + 1

Combine like terms: -8 + 1 = -7
1 + -2x + x2 = -7

Factor a perfect square on the left side:
(x + -1)(x + -1) = -7

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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